We are given that the function $f$ is a one-to-one function. (a) We are given that $f(6) = 9$, and we want to find $f^{-1}(9)$. (b) We are given that $f^{-1}(-2) = -6$, and we want to find $f(-6)$.

1. Problem Description

We are given that the function $f$ is a one-to-one function.

(a) We are given that $f(6) = 9$, and we want to find $f^{-1}(9)$.

(b) We are given that $f^{-1}(-2) = -6$, and we want to find $f(-6)$.

2. Solution Steps

(a) We are given $f(6) = 9$.

The definition of the inverse function is that if $f(x) = y$, then $f^{-1}(y) = x$.

Therefore, if $f(6) = 9$, then $f^{-1}(9) = 6$.

(b) We are given $f^{-1}(-2) = -6$.

Applying the definition of the inverse function, if $f^{-1}(y) = x$, then $f(x) = y$.

Therefore, if $f^{-1}(-2) = -6$, then $f(-6) = -2$.

3. Final Answer

(a) 6

(b) -2